Nikolay Bliznyuk

Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation

We presenta Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given a data vector Y corresponding to the regression model f(β), find plausible values of β. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of β given Y using MCMC. To reduce computational cost, we limit evaluation of f to a small number of points chosen on a high posterior density region found by optimization.Then,we approximate the logarithm of the posterior density using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC.We illustrate our approach on simulated data for a pollutant diffusion problem and study the frequentist coverage properties of credible intervals. Our experiments indicate that our method can produce results similar to those when the true “expensive” posterior density is sampled by MCMC while reducing computational costs by well over an order of magnitude.

Repetitive motor behavior: Further characterization of development and temporal dynamics

Repetitive behaviors are diagnostic for autism spectrum disorders, common in related neurodevelopmental disorders, and normative in typical development. In order to identify factors that mediate repetitive behavior development, it is necessary to characterize the expression of these behaviors from an early age. Extending previous findings, we characterized further the ontogeny of stereotyped motor behavior both in terms of frequency and temporal organization in deer mice. A three group trajectory model provided a good fit to the frequencies of stereotyped behavior across eight developmental time points. Group based trajectory analysis using a measure of temporal organization of stereotyped behavior also resulted in a three group solution. Additionally, as the frequency of stereotyped behavior increased with age, the temporal distribution of stereotyped responses became increasingly regular or organized indicating a strong association between these measures. Classification tree and principal components analysis showed that accurate classification of trajectory group could be done with fewer observations. This ability to identify trajectory group membership earlier in development allows for examination of a wide range of variables, both experiential and biological, to determine their impact on altering the expected trajectory of repetitive behavior across development. Such studies would have important implications for treatment efforts in neurodevelopmental disorders such as autism.

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities

Bayesian inference using Markov chain Monte Carlo (MCMC) is computationally prohibitive when the posterior density of interest, π, is computationally expensive to evaluate. We develop a derivative-free algorithm GRIMA to accurately approximate π by interpolation over its high-probability density (HPD) region, which is initially unknown. Our local approach reduces the waste of computational budget on approximation of π in the low-probability region, which is inherent in global experimental designs. However, estimation of the HPD region is nontrivial when derivatives of π are not available or are not informative about the shape of the HPD region. Without relying on derivatives, GRIMA iterates (a) sequential knot selection over the estimated HPD region of π to refine the surrogate posterior and (b) re-estimation of the HPD region using an MCMC sample from the updated surrogate density, which is inexpensive to obtain. GRIMA is applicable to approximation of general unnormalized posterior densities. To determine the range of tractable problem dimensions, we conduct simulation experiments on test densities with linear and nonlinear component-wise dependence, skewness, kurtosis and multimodality. Subsequently, we use GRIMA in a case study to calibrate a computationally intensive nonlinear regression model to real data from the Town Brook watershed. Supplemental materials for this article are available online.

Nonlinear predictive latent process models for integrating spatio-temporal exposure data from multiple sources

Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related, particles in the greater Boston area. When multiple sources of exposure information are available, a joint model that pools information across sources maximizes data coverage over both space and time, thereby reducing the prediction error. We consider a Bayesian hierarchical framework in which a joint model consists of a set of submodels, one for each data source, and a model for the latent process that serves to relate the submodels to one another. If a submodel depends on the latent process nonlinearly, inference using standard MCMC techniques can be computationally prohibitive. The implications are particularly severe when the data for each submodel are aggregated at different temporal scales. To make such problems tractable, we linearize the nonlinear components with respect to the latent process and induce sparsity in the covariance matrix of the latent process using compactly supported covariance functions. We propose an efficient MCMC scheme that takes advantage of these approximations. We use our model to address a temporal change of support problem whereby interest focuses on pooling daily and multiday black carbon readings in order to maximize the spatial coverage of the study region.

Efficient Interpolation of Computationally Expensive Posterior Densities With Variable Parameter Costs

Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density π of the parameter vector η. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density π is expensive to evaluate. In many such problems, it is possible to identify a minimal subvector β of η responsible for the expensive computation in the evaluation of π. We propose two approaches, DOSKA and INDA, that approximate π by interpolation in ways that exploit this computational structure to mitigate the curse of dimensionality. DOSKA interpolates π directly while INDA interpolates π indirectly by interpolating functions, for example, a regression function, upon which π depends. Our primary contribution is derivation of a Gaussian processes interpolant that provably improves over some of the existing approaches by reducing the effective dimension of the interpolation problem from dim(η) to dim(β). This allows a dramatic reduction of the number of expensive evaluations necessary to construct an accurate approximation of π when dim(η) is high but dim(β) is low. We illustrate the proposed approaches in a case study for a spatio-temporal linear model for air pollution data in the greater Boston area. Supplemental materials include proofs, details, and software implementation of the proposed procedures.

Uncertainty Analysis for Computationally Expensive Models with Multiple Outputs

Bayesian MCMC calibration and uncertainty analysis for computationally expensive models is implemented using the SOARS (Statistical and Optimization Analysis using Response Surfaces) methodology. SOARS uses a radial basis function interpolator as a surrogate, also known as an emulator or meta-model, for the logarithm of the posterior density. To prevent wasteful evaluations of the expensive model, the emulator is built only on a high posterior density region (HPDR), which is located by a global optimization algorithm. The set of points in the HPDR where the expensive model is evaluated is determined sequentially by the GRIMA algorithm described in detail in another paper but outlined here. Enhancements of the GRIMA algorithm were introduced to improve efficiency. A case study uses an eight-parameter SWAT2005 (Soil and Water Assessment Tool) model where daily stream flows and phosphorus concentrations are modeled for the Town Brook watershed which is part of the New York City water supply. A Supplemental Material file available online contains additional technical details and additional analysis of the Town Brook application.

The development of repetitive motor behaviors in deer mice: Effects of environmental enrichment, repeated testing, and differential mediation by indirect basal ganglia pathway activation

Little is known about the mechanisms mediating the development of repetitive behaviors in human or animals. Deer mice reared with environmental enrichment (EE) exhibit fewer repetitive behaviors and greater indirect basal ganglia pathway activation as adults than those reared in standard cages. The developmental progression of these behavioral and neural circuitry changes has not been characterized. We assessed the development of repetitive behavior in deer mice using both a longitudinal and cohort design. Repeated testing negated the expected effect of EE, but cohort analyses showed that progression of repetitive behavior was arrested after 1 week of EE and differed significantly from controls after 3 weeks. Moreover, EE reductions in repetitive behavior were associated with increasing activation of indirect pathway nuclei in males across adolescence, but not females. These findings provide the first assessment of developmental trajectories within EE and support indirect pathway mediation of repetitive behavior in male deer mice.

Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes

In many studies, the distribution of soil attributes depends on both spatial location and environmental factors, and prediction and process identification are performed using existing methods such as kriging. However, it is often too restrictive to model soil attributes as dependent on a known, parametric function of environmental factors, which kriging typically assumes. This paper investigates a semiparametric approach for identifying and modeling the nonlinear relationships of spatially dependent soil constituent levels with environmental variables and obtaining point and interval predictions over a spatial region. Frequentist and Bayesian versions of the proposed method are applied to measured soil nitrogen levels throughout Florida, USA and are compared to competing models, including frequentist and Bayesian kriging, based an array of point and interval measures of out-of-sample forecast quality. The semiparametric models outperformed competing models in all cases. Bayesian semiparametric models yielded the best predictive results and provided empirical coverage probability nearly equal to nominal.

Enteral Feeding as an Adjunct to Hypothermia in Neonates with Hypoxic-Ischemic Encephalopathy

Background: Withholding enteral feedings during hypothermia lacks supporting evidence. Objectives: We aimed to determine if minimal enteral nutrition (MEN) during hypothermia in patients with hypoxic-ischemic encephalopathy was associated with a reduced duration of parenteral nutrition, time to full oral feeds, and length of stay, but would not be associated with increased systemic inflammation or feeding complications. Methods: We performed a pilot, retrospective, matched case-control study within the Florida Neonatal Neurologic Network from December 2012 to May 2016 of patients who received MEN during hypothermia (n = 17) versus those who were not fed (n = 17). Length of stay, feeding-related outcomes, and brain injury identified by MRI were compared. Serum inflammatory mediators were measured at 0–6, 24, and 96 h of life by multiplex assay. MRI were scored using the Barkovich system. Results: MEN subjects had a reduced length of hospital stay (mean 15 ± 11 vs. 24 ± 19 days, p < 0.05), days receiving parenteral nutrition (7 ± 2 vs. 11 ± 6, p < 0.05), and time to full oral feeds (8 ± 5 vs. 18 ± 18, p < 0.05). MEN was associated with a significantly reduced serum IL-12p70 at 24 and 96 h (p < 0.05). Brain MRI scores were not significantly different between groups. Conclusion: MEN during hypothermia was associated with a reduced length of stay and time to full feeds, but did not increase feeding complications or systemic inflammation.

A Pilot Study of Inhaled CO Therapy in Neonatal Hypoxia-Ischemia: Carboxyhemoglobin Concentrations and Brain Volumes

Objective: The objective of this pilot study was to start evaluating the efficacy and the safety (i.e., carboxyhemoglobin concentration of carbon monoxide (CO)) as a putative neuroprotective therapy in neonates. Study Design: Neonatal C57BL/6 mice were exposed to CO at a concentration of either 200 or 250 ppm for a period of 1 h. The pups were then sacrificed at 0, 10, 20, 60, 120, 180, and 240 min after exposure to either concentration of CO, and blood was collected for analysis of carboxyhemoglobin. Following the safety study, 7-day-old pups underwent a unilateral carotid ligation. After recovery, the pups were exposed to a humidified gas mixture of 8% oxygen and 92% nitrogen for 20 min in a hypoxia chamber. One hour after the hypoxia exposure, the pups were randomized to one of two groups: air (HI+A) or carbon monoxide (HI+CO). An inhaled dose of 250 ppm of CO was administered to the pups for 1 h per day for a period of 3 days. At 7 days post-injury, the pups were sacrificed and the brains analyzed for cortical and hippocampal volumes. Results: CO exposure at 200 and 250 ppm produced a peak carboxyhemoglobin concentration of 21.52 ± 1.18% and 27.55 ± 3.58%, respectively. The carboxyhemoglobin concentrations decreased rapidly, reaching control concentrations by 60 min post exposure. At 14 days of age (7 days post injury), the HI+CO (treated with 1 h per day of 250 ppm of CO for 3 days post injury) had significant preservation of the ratio of ipsilateral to contralateral cortex (median 1.07, 25% 0.97, 75% 1.23, n = 10) compared the HI+A group (p < 0.05). Conclusion: CO exposure of 250 ppm did not reach carboxyhemoglobin concentrations which would induce acute neurologic abnormalities and was effective in preserving cortical volumes following hypoxic-ischemic injury.